6 results
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2. A Collective Neurodynamic Optimization Approach to Nonnegative Matrix Factorization.
- Author
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Fan, Jianchao and Wang, Jun
- Subjects
- *
FACTORIZATION , *MATHEMATICAL optimization - Abstract
Nonnegative matrix factorization (NMF) is an advanced method for nonnegative feature extraction, with widespread applications. However, the NMF solution often entails to solve a global optimization problem with a nonconvex objective function and nonnegativity constraints. This paper presents a collective neurodynamic optimization (CNO) approach to this challenging problem. The proposed collective neurodynamic system consists of a population of recurrent neural networks (RNNs) at the lower level and a particle swarm optimization (PSO) algorithm with wavelet mutation at the upper level. The RNNs act as search agents carrying out precise local searches according to their neurodynamics and initial conditions. The PSO algorithm coordinates and guides the RNNs with updated initial states toward global optimal solution(s). A wavelet mutation operator is added to enhance PSO exploration diversity. Through iterative interaction and improvement of the locally best solutions of RNNs and global best positions of the whole population, the population-based neurodynamic systems are almost sure able to achieve the global optimality for the NMF problem. It is proved that the convergence of the group-best state to the global optimal solution with probability one. The experimental results substantiate the efficacy and superiority of the CNO approach to bound-constrained global optimization with several benchmark nonconvex functions and NMF-based clustering with benchmark data sets in comparison with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
3. Backward Mean-Field Linear-Quadratic-Gaussian (LQG) Games: Full and Partial Information.
- Author
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Huang, Jianhui, Wang, Shujun, and Wu, Zhen
- Subjects
- *
STOCHASTIC differential equations , *MEAN field theory , *GAME theory , *DATA structures , *MATHEMATICAL optimization - Abstract
This paper introduces the
backward mean-field (MF) linear-quadratic-Gaussian (LQG) games (for short, BMFLQG) of weakly coupled stochastic large-population system. In contrast to the well-studiedforward mean-field LQG games, the individual state in our large-population system follows the backward stochastic differential equation (BSDE) whoseterminal insteadinitial condition should be prescribed. Two classes of BMFLQG games are discussed here and their decentralized strategies are derived through the consistency condition. In the first class, the individual agents of large-population system are weakly coupled in their state dynamics and the full information can be accessible to all agents. In the second class, the coupling structure lies in the cost functional with only partial information structure. In both classes, the asymptotic near-optimality property (namely, $\epsilon$- Nash equilibrium) of decentralized strategies are verified. To this end, some estimates to BSDE, are presented in the large-population setting. [ABSTRACT FROM AUTHOR]- Published
- 2016
- Full Text
- View/download PDF
4. Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control.
- Author
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Grammatico, Sergio, Parise, Francesca, Colombino, Marcello, and Lygeros, John
- Subjects
- *
DECENTRALIZED control systems , *AUTOMATIC control systems , *NASH equilibrium , *MATHEMATICAL optimization , *MULTIAGENT systems , *STOCHASTIC convergence , *MEAN field theory - Abstract
This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
5. Gaussian Classifier-Based Evolutionary Strategy for Multimodal Optimization.
- Author
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Dong, Wenyong and Zhou, MengChu
- Subjects
- *
GAUSSIAN distribution , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *DISTRIBUTION (Probability theory) , *MATHEMATICAL models - Abstract
This paper presents a Gaussian classifier-based evolutionary strategy (GCES) to solve multimodal optimization problems. An evolutionary technique for them must answer two crucial questions to guarantee its success: how to distinguish among the different basins of attraction and how to safeguard the already discovered good-quality solutions including both global and local optima. In GCES, multimodal optimization problems are regarded as classification ones, and Gaussian mixture models are employed to save the locations and basins of already and presently identified local or global optima. A sequential estimation technique for the covariance of a Gaussian model is introduced into GCES. To best adjust the global step size, a strategy named top-ranked sample selection is introduced, and a classification method instead of a common but problematic radius-triggered manner is proposed. Experiments are performed on a series of benchmark test functions to compare GCES with the state-of-the-art multimodal optimization approaches. The results show that GCES is not only simple to program and understand, but also provides better and consistent performance. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
6. Risk-Sensitive Mean-Field Games.
- Author
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Tembine, Hamidou, Zhu, Quanyan, and Basar, Tamer
- Subjects
- *
DIFFERENTIAL games , *COST functions , *MATHEMATICAL optimization , *NUMERICAL analysis , *GAME theory - Abstract
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton –Jacobi– Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean–Vlasov equations, Fokker–Planck–Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean–Vlasov dynamics. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
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